From dedb4d23f3a6d4dc502cc45eb89805d763ae8bf4 Mon Sep 17 00:00:00 2001 From: Jack Halford Date: Fri, 31 May 2024 21:22:24 +0200 Subject: [PATCH] change paths --- {LL1 => 1}/1-generalized-co-ordinates.md | 0 {LL1 => 1}/10-mechanical-similarity.md | 0 {LL1 => 1}/10_problems.md | 0 {LL1 => 1}/11-motion-in-one-dimension.md | 0 {LL1 => 1}/11_problems.md | 0 ...potential-energy-from-the-period-of-oscillation.md | 0 {LL1 => 1}/13-the-reduced-mass.md | 0 {LL1 => 1}/13_problem.md | 0 {LL1 => 1}/14-motion-in-a-central-field.md | 0 {LL1 => 1}/2-the-principle-of-least-action.md | 0 {LL1 => 1}/3-galileos-relativity-principle.md | 0 {LL1 => 1}/4-the-lagrangian-for-a-free-particle.md | 0 .../5-the-lagrangian-for-a-system-of-particles.md | 11 ++++++++++- {LL1 => 1}/5_problems.md | 0 {LL1 => 1}/6-energy.md | 0 {LL1 => 1}/7-momentum.md | 0 {LL1 => 1}/7_problem.md | 0 {LL1 => 1}/8-centre-of-mass.md | 0 {LL1 => 1}/8_problem.md | 0 {LL1 => 1}/9-angular-momentum.md | 0 {LL1 => 1}/9_problems.md | 0 {LL1 => 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LL1/3-galileos-relativity-principle.md rename to 1/3-galileos-relativity-principle.md diff --git a/LL1/4-the-lagrangian-for-a-free-particle.md b/1/4-the-lagrangian-for-a-free-particle.md similarity index 100% rename from LL1/4-the-lagrangian-for-a-free-particle.md rename to 1/4-the-lagrangian-for-a-free-particle.md diff --git a/LL1/5-the-lagrangian-for-a-system-of-particles.md b/1/5-the-lagrangian-for-a-system-of-particles.md similarity index 97% rename from LL1/5-the-lagrangian-for-a-system-of-particles.md rename to 1/5-the-lagrangian-for-a-system-of-particles.md index 819f95e..5c818da 100644 --- a/LL1/5-the-lagrangian-for-a-system-of-particles.md +++ b/1/5-the-lagrangian-for-a-system-of-particles.md @@ -4,6 +4,8 @@ title: 5. The Lagrangian for a system of particles Let us now consider a system of particles which interact with one another but with no other bodies. This is called a closed system. It is found that the interaction between the particles can be described by adding to the Lagrangian `LL1/4.2` for non-interacting particles a certain function of the co-ordinates, which depends on the nature of the interaction[^1]. Denoting this function by $-U$, we have +[^1]: This statement is valid in classical mechanics. Relativistic mechanics is not considered in this book. (See `LL2`) + ```load LL1/5.1 ``` @@ -84,4 +86,11 @@ LL1/5.8 To conclude this section, we may make the following remarks concerning the application of Lagrange's equations to various problems. It is often necessary to deal with mechanical systems in which the interaction between different bodies (or particles) takes the form of constraints, i.e. restrictions on their relative position. In practice, such constraints are effected by means of rods, strings, hinges and so on. This introduces a new factor into the problem, in that the motion of the bodies results in friction at their points of contact, and the problem in general ceases to be one of pure mechanics `LL1/25`. In many cases, however, the friction in the system is so slight that its effect on the motion is entirely negligible. If the masses of the constraining elements of the system are also negligible, the effect of the constraints is simply to reduce the number of degrees of freedom $S$ of the system to a value less than $3N$. To determine the motion of the system, the Lagrangian `LL1/5.5` can again be used, with a set of independent generalised co-ordinates equal in number to the actual degrees of freedom. -[^1]: This statement is valid in classical mechanics. Relativistic mechanics is not considered in this book. (See `LL2`) +## Problems + +Find the Lagrangian for each of the following systems when placed in a uniform gravitational field (acceleration $g$). + +#### PROBLEM 1. 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a/LL1/equations/9.8.tex b/1/equations/9.8.tex similarity index 100% rename from LL1/equations/9.8.tex rename to 1/equations/9.8.tex diff --git a/LL1/toc.md b/1/index.md similarity index 98% rename from LL1/toc.md rename to 1/index.md index 63099a2..1a269fe 100644 --- a/LL1/toc.md +++ b/1/index.md @@ -1,6 +1,7 @@ --- title: Mechanics subtitle: | + Course of Theoretical Physics, Volume 1 By L. D. Landau and E. M. Lifschitz Translated from the Russian by J. B. Sykes and J. S. Bell --- diff --git a/Makefile b/Makefile index eeec58d..a4fc71f 100644 --- a/Makefile +++ b/Makefile @@ -1,4 +1,4 @@ -MD = $(shell ls LL1/*.md) +MD = $(shell ls 1/*.md) HTML = $(addprefix out/,$(MD:.md=.html)) GOATCOUNTER = $(or $(PROD),false) diff --git a/README.md b/README.md index 3c75c45..9757772 100644 --- a/README.md +++ b/README.md @@ -5,5 +5,5 @@ ## Mistakes? -LL2. expression before 9.10, denominator is ds not sqrt(ds) -LL3. between 4.6 and 4.7, I think that fg-gf is anti-Hermitian iff f and g are Hermitian +- LL2. expression before 9.10, denominator is ds not sqrt(ds) +- LL3. between 4.6 and 4.7, I think that fg-gf is anti-Hermitian iff f and g are Hermitian diff --git a/tools/pf-filter.py b/tools/pf-filter.py index 9f129c3..c3a87a5 100644 --- a/tools/pf-filter.py +++ b/tools/pf-filter.py @@ -42,11 +42,7 @@ def action(elem, doc): title = [l for l in open(f"{book}/{slug}", 'r').readlines() if l.startswith('title:')][0] title = title.strip("title: ") slug = slug.replace(".md", ".html") - html = f''' - - §{title} - - ''' + html = f'§{title.strip('\n')}' elem = pf.RawInline(html, format='html') return elem else: diff --git a/tools/template.html b/tools/template.html index b285da0..6607973 100644 --- a/tools/template.html +++ b/tools/template.html @@ -64,7 +64,7 @@ $endif$